Continuity mistake: When Doug is ringing Arthur at the beginning of the episode, there are 2 lunch boxes on top of the lockers behind Doug. During different shots 1 disappears and reappears. (00:00:45)
Continuity mistake: At the start there are 2 letters on the table in front of Arthur. When Doug rings for the 3rd time they have disappeared. (00:00:50)
Continuity mistake: When Doug spots the chicken he has his gun down by his side in the first shot and raised in the second shot. (00:18:40)
Visible crew/equipment: During Spence and Danny's fight scene, there are a couple of shots where you can see Danny's mic pack on his belt. (00:16:20)
Visible crew/equipment: In the garage, when Spence says "so Deacon" there is a shot of Danny in the chair with a taper marker in front of him. (00:06:30)
Hi Def-Jam - S3-E13
Continuity mistake: When Doug is seeing the HD TV for the first time, he's holding his PDA in two hands which then becomes one hand when the camera has changed to a different angle. (00:02:20)
Hi Def-Jam - S3-E13
Continuity mistake: At the start Carrie is holding an egg in two hands or one hand depending on the camera angle. (00:00:42)
Continuity mistake: After Carrie says she's taking Doug's camera to her office party, the box magically appears on her lap. (00:09:50)
Continuity mistake: When Carrie gets her camera it changes position in her hands before she turns it around. Note the strap, it goes from left to right. (00:06:00)
Continuity mistake: When Doug goes to get Carrie's present from the closet her position on the bed changes between shots. (00:05:30)
Continuity mistake: When we first see Lou, he is pushing some rubbish down into the bin, camera cuts and he now has a box in his hand. (00:00:05)
Continuity mistake: Carrie asks Doug what he's doing when she walks into the bedroom. She then hangs her coat on a hanger and has the coat in her hands (as seen in her reflection in the mirror). Camera changes and she's shutting the wardrobe. (00:08:01)
Continuity mistake: When Doug and Deacon both volunteer for the calendar the magazine on the bench is constantly changing position without being touched. (00:05:10)
Strike Out - S3-E7
Continuity mistake: The bottle of Lipton Ice Tea on the table rotates on its own without anyone touching it. (00:03:20)
Strike Too - S3-E6
Continuity mistake: When Carrie puts her bag on at the start it swaps arms instantly. (00:02:30)
Strike Too - S3-E6
Continuity mistake: At the start when Doug is having his breakfast something appears on top of his pancakes. (00:00:30)
Strike One - S3-E5
Continuity mistake: When Carrie says about smelling like the F train she has her hands together in front of her chest. When the camera changes angle, her hands are spread. (00:16:20)
Strike One - S3-E5
Visible crew/equipment: When Doug is listing all the extras for the truck, you can see tape markers on the floor behind them. Specifically, one in between the feet of an extra that is standing behind them. (00:08:50)
Visible crew/equipment: When the dummy is on the sofa with Arthur, the stage lights are reflected in its sunglasses. (00:16:00)
Visible crew/equipment: When Doug says about Carrie's laugh he sits down on the sofa. As he does, part of the set lights are visible above him. (00:15:20)
Answer: To answer the question directly. Carrie and Doug do not have a biological child during the show's main run. In season 3 or 4 finale (cant remember which) Carrie has a miscarriage. Later on in the show they find out Carrie has 1 working ovary. Thus reducing the chance of them conceiving. By the final season, they couple agree to adopt from China and go to collect their child in the show's final episode. While on the flight back from China it's revealed that Carrie is once again pregnant. However the last scene of the show is a flash forward showing that Carrie goes full term with that child and they are struggling with both kids.
Ssiscool ★
Adding on to this answer, I read somewhere that producers were afraid of the show having a "before baby" feeling and then an "after baby" feeling. Some fans feel that main characters, or the show in general, decline in quality after a major change. For example, Jesse and Rebecca on "Full House" after they had twin sons, and Daphne on "Frasier" after she married Niles.